For example, we have a few dogs within the Happy Pets family that suffer from various degrees of anxiety. This ranges from fear of people in the home, fear of the outdoors, and fear of strangers. Dogs often respond to fear by barking, which is often misinterpreted as aggression. Barking is a dog's way of telling a person, or another dog, to keep their distance. The biggest mistake someone can make is to try to force a barking dog to do something they are scared of. Sometimes the best course of action is just to wait them out. Once they see you don't pose a threat, their curiosity (and noses) will take over, and they will break out of their shell.
I often tell my staff to offer a treat (smells good!) and let the dog come to them. Don't overestimate the power of just sitting and letting the dog smell you first. A few other tips that I've found helpful are avoiding direct eye contact or staring as well as turning the body slightly to the side. The dog will not be as threatened if your body language is less domineering and aggressive.
So, what do you do if your fearful pet is of the feline persuasion? Many of the same tips still apply! Sit down and let the cat come to you. Avoid trying to pet them right away. You can also gain trust with a cat by using the slow blink technique. Cats only close their eyes around people they trust. By making eye contact with the fearful kitty and engaging in slow blinking (slowly close your lids and hold closed for a few second, before slowly opening again). Cats are natural mimics, and will soon follow suit. This trust building exercise will soon have your fearful feline purring in no time.